draft ecology metrics

new_metrics.R

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+## Minimal spanning tree distances evenness
+func.eve <- function(matrix) {
+    ## Distance matrix
+    distances <- dist(matrix)
+    ## weighted evenness (EW) for equal weighted species
+    branch_lengths <- (distances/2)[which(as.dist(ape::mst(distances)) != 0)]
+    ## partial weighted evenness (PEW)
+    rel_br_lentghs <- branch_lengths/sum(branch_lengths)
+    ## Regular abundance value (1/(S-1))
+    regular <- 1/(nrow(matrix) - 1)
+    ## Get the minimal distances
+    min_distances <- sapply(rel_br_lentghs, function(x, y) min(c(x, y)), y = regular)
+    ## Return the Functional eveness
+    return((sum(min_distances) - regular) / (1 - regular))
+}
+
+## Distance from centroid deviation ratio
+func.div <- function(matrix) {
+    ## The distance from centroid (dGi)
+    dist_centroid <- centroids(matrix)
+    ## The mean distance from centroid (dG)
+    mean_dis_cent <- mean(dist_centroid)
+    ## The number of observations
+    obs <- length(dist_centroid)
+    ## The FDiv metric
+    return((sum(dist_centroid) - mean_dis_cent * (obs-1)) / ((sum(abs(dist_centroid - mean_dis_cent) + dist_centroid))/obs))
+}
+
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+
+test_that("ecology.metric", {
+    set.seed(1)
+    dummy_matrix <- matrix(rnorm(25),5,5, dimnames = list(letters[1:5]))
+    x <- dist(dummy_matrix)
+    x_pco <- cmdscale(as.matrix(x), k = ncol(as.matrix(x))-1)
+
+    library(FD)
+    FD_test <- dbFD(x)
+
+    ## Convex Hull volume
+    expect_equal(geometry::convhulln(x_pco, "FA")$vol, FD_test$FRic)
+
+    ## Regularity of distances on the minimum spanning tree (Villéger et al. 2008)
+    expect_equal(func.eve(x_pco), FD_test$FEve)
+
+    ## Distance from centroid deviation ratio (Villéger et al. 2008)
+    expect_equal(func.div(x_pco), FD_test$FDiv)
+
+})
+
+
+FDis <- FD_test$FDis # Laliberté and Legendre 2010 - Functional dispersion = Average distance to centroid (if all species have the same abundance) =  multivariate dispersion - Anderson (2006))
+# mean(centroids(as.matrix(x)))
+func.disp <- function(matrix){unname(FD::fdisp(dist(matrix))$FDis)}
+
+
+mean(centroids(as.matrix(x)))
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+RaoQ <- FD_test$RaoQ # Rao's quadratic entropy (Q) - Botta-Dukát (2005)
+ade4::divc(data.frame(matrix(1, ncol = 1, nrow = nrow(as.matrix(x)), dimnames = list(c(rownames(as.matrix(x)))))),
+            x, scale = FALSE)
+
+
+# # Villéger, S., N. W. H. Mason and D. Mouillot (2008) New multidimensional functional diversity indices for a multifaceted framework in functional ecology. Ecology 89:2290-2301.
+# # Legendre, P. and L. Legendre (1998) Numerical Ecology. 2nd English edition. Amsterdam: Elsevier.
+# # Laliberté, E. and P. Legendre (2010) A distance-based framework for measuring functional diversity from multiple traits. Ecology 91:299-305.
+# # Anderson, M. J. (2006) Distance-based tests for homogeneity of multivariate dispersions. Biometrics 62:245-253.
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